Two-dimensional nonlinear beam shaping

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.     

On‐axis shaping of second‐harmonic beams

We report complete spatial shaping (both phase and amplitude) of the second‐harmonic beam generated in a nonlinear photonic crystal. Using a collinear second‐order process in a nonlinear computer generated hologram imprinted on the crystal, the desired beam is generated on‐axis and in the near field. This enables compact and efficient one‐dimensional beam shaping in comparison to previously demonstrated off‐axis Fourier holograms. We experimentally demonstrate the second‐harmonic generation of high‐order Hermite–Gauss, top hats and arbitrary skyline‐shaped beams.

     

Analytical structure of Hermite Gaussian beam in far field

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical structure of Hermite Gaussian beam in far field is presented. The structural energy flux distributions are also investigated in the far field. The structural pictures of some Hermite Gaussian beams are depicted in the far field. As the structure of Hermite Gaussian beam is dominated by the transverse mode numbers and the initial transverse Gaussian half width, it is more complex than that of Gaussian beam. The ratios of the structural energy fluxes to the whole energy flux are independent of the transverse mode numbers and the initial transverse Gaussian half width. The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.\     

大气湍流中光束束宽扩展和角扩展的比较研究

以厄米-双曲余弦-高斯（H-ChG）光束为例,对H-ChG光束通过大气湍流传输时的束宽扩展和角扩展做了详细研究.用相对束宽和相对角扩展代替束宽和角扩展来研究湍流对光束影响的灵敏程度.研究表明,折射率结构常数C²_n越小,光束束宽扩展和角扩展越小.有较大阶数m,n,较小参数Ω₀和束腰宽度w₀ H-ChG光束的角扩展受湍流影响较小.当传输距离足够远时,这一结论对H-ChG光束的束宽扩展也成立.当传输距离不长时,对H-ChG光束相对束宽随Ω₀和w₀的变化规律做了分析.用数值计算例做了说明,并对结果的正确性做了物理解释.厄米-高斯,双曲余弦高斯和高斯光束在大气湍流中的扩展可作为H-ChG光束的特例来处理. 关键词： 束宽扩展和角扩展 大气湍流 厄米-双曲余弦-高斯光束     

Propagation of elegant Hermite cosine Gaussian laser beams

In this paper, a more generalized beam containing an elegant Hermite Gaussian beam and a cosine Gaussian beam, which is called elegant Hermite cosine Gaussian (EHcoG) beam, is introduced and studied. The propagation properties of the EHcoG laser beams through a first-order paraxial optical system are demonstrated analytically and numerically. The recurrence propagation equations of the EHcoG beams through a first-order paraxial optical system with and without aperture are derived, from which the analytical propagation expression for EHcoG beams of any order can be obtained by means of the recursive procedures. The validity of the analytical results is confirmed by the numerical results.     

Propagation properties of Airy–Gaussian beams

The propagation of the Airy–Gaussian beams is studied in strongly nonlocal nonlinear media analytically and numerically. The linear momentum of the analytical Airy–Gaussian beam solution of the Snyder–Mitchell model is not conservational, which is the reason that results in the disagreement between the analytical Airy–Gaussian beam solution and the numerical simulations of the nonlocal nonlinear Schr?dinger equation in the case of strong nonlocality. The quasi-Airy–Gaussian soliton in the Gaussian-shaped response material can be obtained when the parameter χ ₀ is large enough, and the patterns of Airy–Gaussian beams are variable periodically in liquid crystal material during propagation.     

Beam divergence effects on high power optical parametric oscillation

The beam divergence effects of the input pump laser on a high power nanosecond optical parametric oscillator （OPO） have been numerically simulated. The OPO conversion efficiency is affected due to the angular deviation of real laser beams from ideal phase matching conditions. Our theoretical model is based on the decomposition of the Gaussian beam and assumes each component has a single deviation angle and thus a particular wave vector mismatch. We take into account the variable intensity profile in the spatial and temporal domains of the Gaussian beam, the pump depletion effects for large-signal processes as well as the oscillatory effects of the three waves. Two nonlinear crystals β-BaB2O4 （BBO） and LiB305 （LBO） have been investigated in detail. The results indicate that the degree of beam divergence strongly influences the maximum pump intensity, optimum crystal length and OPO conversion efficiency. The impact of beam divergence is much more severe in the case of critical phase-matching for BBO than in the case of non-critical phase-matching for LBO. The results provide a way to choose the optimum parameters for a high power ns OPO such as the nonlinear material, the crystal length and the pump intensity, etc. Good agreement is obtained with our experimental results.     

Generation of hollow Gaussian beams by spatial filtering

We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.     

Second-harmonic power of KTiOPO4 with double refraction

Second harmonic (SH) power of the type-II phase matching in KTiOPO₄ (KTP) is calculated for the fundamental beams of TEM₀₀ mode within the near field approximation (parallel Gaussian beam) taking the beam walk-off effect among the two fundamental and the SH beams into account. The slit intensity and the total SH power are calculated as functions of the beam radius and the crystal length. Two approximations are made for the SH power calculation at tight beam focusing condition. The measurements of the SH power in KTP are carried out for three crystals of 6, 3, and 1.5 mm thickness. The effective nonlinear coefficient for Nd: YAG incident radiation is estimated to be 4.3 pm/V with 10% uncertainty, taking the enhancement factor due to the multimode structure of the laser beam into account.     

多艾里光束合成自聚焦光束的实验实现

多光束合成和单光束聚焦一直是提高激光束功率和功率密度的两个重要方法. 结合艾里光束在自由空间中沿弯曲路径传播的特性, 从数值模拟和实验两个方面, 研究了利用多个一维艾里光束合成自由空间自聚焦光束的方法, 并对所得到的模拟和实验结果进行了对比. 采用分步束传播法, 分别模拟了由四个和八个一维艾里光束合成的自聚焦光束在自由空间中的传播过程, 给出了自聚焦光束在传播过程中横向和纵向的光强分布和变化趋势. 采用计算全息和空间光调制器技术实验, 实现了多个一维艾里光束合成的自聚焦光束. 实验中分别测量了四个和八个一维艾里光束合成的自聚焦光束的横向光强分布. 实验结果和理论结果符合得较好. 另外, 为了进一步增大自聚焦光束的功率, 可以增加参与合成的一维艾里光束的数量. 同时, 自聚焦光束的焦距可以通过调整各个一维艾里光束的相对位置进行调节.     

Gyrator transform of Gaussian beams with phase difference and generation of hollow beam

The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω₀. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.     

Vectorial structure of the far field of an elegant Hermite–Gaussian beam

Based on the vector angular spectrum method and the method of stationary phase, an analytical expression for the vectorial structure of the far field of an elegant Hermite–Gaussian beam is derived. The analytical formulae of the energy flux distributions of the TE term, the TM term, and the whole beam are presented in the far field. Analytical expressions for the ratios of the powers of the TE and TM terms to those of the elegant Hermite–Gaussian beam are obtained without any approximation. The physical pictures of the far field of an elegant Hermite–Gaussian beam are demonstrated and compared with those of the far field of the corresponding standard Hermite–Gaussian beam. This research reveals the internal vectorial structure of the far field of an elegant Hermite–Gaussian beam from an alternative viewpoint.     

Experimental measurement of covariance matrix of two-mode entangled state

A two-mode entangled state was generated experimentally through mixing two squeezed lights from two optical parametric amplifiers on a 50/50 beam splitter.The entangled beams were measured by means of two pairs of balanced homodyne detection systems respectively.The relative phases between the local beams and the detected beams can be locked by using the optical phase modulation technique.The covariance matrix of the two-mode entangled state was obtained when the relative phase of the local beam and the detected beam in one homodyne detection system is locked and the other is scanned.This method provides a way by which one can extract the covariance matrix of any selected quadrature components of two-mode Gaussian state.     

对称化光学系统对像散复宗量厄米-高斯光束的变换

 使用二阶矩和广义惠更斯 菲涅尔衍射积分方法研究了用于实宗量厄米高斯光束对称化的光学系统对复宗量厄米-高斯光束的变换。研究结果表明：复宗量厄米-高斯光束经过该光学系统后，只能在出射面上实现在二阶矩定义下的对称化，但光斑不具有旋转对称性。因此，这套用于实宗量光束对称化的光学系统对复宗量光束并不适用。     

Dynamically reconfigurable characteristics of a double phase conjugate mirror using Sn2P2S6 crystals and their application to optical inter-satellite communication

A double phase conjugate mirror (DPCM), created by two mutually incoherent beams entering photorefractive nonlinear materials, can generate a phase conjugate beam whose reflectivity may be greater than 100%. Even though the conditions of the incident beams are changed, the DPCM can be dynamically reconfigured by using a Sn₂P₂S₆ crystal with a high response speed. These features of the DPCM are advantageous, particularly in an optical inter-satellite communication system. In particular, use of the phase conjugate beam from the DPCM offers wavefront compensation and amplification in satellite communication. In addition, the dynamically reconfigurable DPCM using a Sn₂P₂S₆ crystal relaxes the acquisition accuracy of the signal beam in the system. In this study, the temporal and spatial operating characteristics of the DPCM using a Sn2P2S6 crystal were first clarified. Next, an inter-satellite system based on the DPCM was proposed, and it was demonstrated that our system significantly improves the tolerance of the acquisition accuracy and tracking time.     

Generation of TE- and TH-polarized Bessel beams using one-dimensional photonic crystal

Based on the matrix method, a theory of propagation of TE- and TH-polarized Bessel light beams (BLBs) in a one-dimensional photonic crystal (1DPC) is developed. The transmission through a 1DPC (with and without a defect impurity) of a quasi-circularly-polarized incident Bessel beam generated by an axicon from a circularly-polarized Gaussian beam has been calculated and analyzed. Also a solution of the problem on the transmission of BLBs through crystalline plate (layer of a uniaxial crystal with the orientation of the optical axis orthogonally to its interfaces) and reflection from it has been presented.Based on this, a new method of formation of TE- and TH-polarized Bessel light beams has been proposed. It has been shown that it is possible to control this process by changing the cone angle of an incident Bessel light beam. The effect of generation of a coherent superposition of two Bessel beams with different cone angles in the case of a high birefringence of defect layer has been predicted theoretically.     

Instability analysis of Gaussian beam propagation in a nonlinear refractive index medium

In this paper, we use a thin filament two dimensional Gaussian beam to model the self-trapping filament. The instability of the propagation of a Gaussian beam through a nonlinear refractive index media is investigated, theoretically and numerically. Specifically, the small scale instability of the beam is examined. The numerical results show that the propagation of the two dimensional Gaussian beam presents one or more nonlinear focal points.      

Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media

We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.     

厄米-余弦-高斯光束的传输特性

 从广义惠更斯-菲涅耳衍射积分出发对厄米-余弦-高斯光束的传输特性作了研究，给出了厄米-余弦-高斯光束通过近轴ABCD光学系统的解析传输公式，以厄米-余弦-高斯光束通过自由空间和薄透镜系统为例做了数值计算和分析，结果表明厄米-余弦-高斯光束在自由空间传输时不能保持其形状不变。厄米-双曲余弦-高斯光束、余弦-高斯光束、厄米-高斯光束的传输公式可作为厄米-余弦-高斯光束的特例得出。     

厄米-高斯光束的M2因子矩阵

提出了厄米-高斯光场的M²因子矩阵.引入束半宽平方的交叉项、M²因子的交叉项,理论推导出了在同一坐标系下光场旋转一定角度后的M²因子矩阵,数值模拟了与M²因子矩阵有关的各参数随光场旋转角度变化的规律,给出了光场的M²因子矢量点随光场旋转角度变化的轨迹曲线.计算结果与理论推导结果相符,证实了利用M²因子矩阵可以将旋转前后的二维厄米-高斯光场用旋转矩阵统一起来.该方法可推广到对一般的二维高阶高斯光束的光束质量的理论分析上,具有普适性,对光束质量的实际测量有重要的理论指导意义. 关键词： M²因子矩阵')" href="#">M²因子矩阵 厄米-高斯光束 非对称激光束 矩阵光学